Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers...

In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers....

Additive number theory is the subfield of number theory concerning the study of subsets of integers and their behavior under addition. More abstractly...

Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations...

number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory...

Prime number theory may refer to: Prime number Prime number theorem Number theory Fundamental theorem of arithmetic, which explains prime factorization...

In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because...

Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation...

Gauss's lemma in number theory gives a condition for an integer to be a quadratic residue. Although it is not useful computationally, it has theoretical...

discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential...

Multiplicative number theory is a subfield of analytic number theory that deals with prime numbers and with factorization and divisors. The focus is usually...

smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime...

topics in number theory. See also: List of recreational number theory topics Topics in cryptography Composite number Highly composite number Even and odd...

force. Thus, string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions...

modern number theory include elementary number theory, analytic number theory, algebraic number theory, and geometric number theory. Elementary number theory...

In mathematics, Probabilistic number theory is a subfield of number theory, which explicitly uses probability to answer questions about the integers and...

Unsolved Problems in Number Theory may refer to: Unsolved problems in mathematics in the field of number theory. A book with this title by Richard K. Guy...

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any...

Measure theory — Model theory — Module theory — Morse theory — Nevanlinna theory — Number theory — Obstruction theory — Operator theory — Order theory — PCF...

coefficients. algebraic number field See number field. algebraic number theory Algebraic number theory analytic number theory Analytic number theory Artin The Artin...

Originally a part of number theory and analysis, partition theory is now considered a part of combinatorics or an independent field. Order theory is the study...

mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures)...

In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive...

study or usage is called arithmetic, a term which may also refer to number theory, the study of the properties of numbers. Besides their practical uses...

for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem for an example). Unlike real functions...

is "an arithmetic version of Teichmüller theory for number fields equipped with an elliptic curve". The theory was made public in a series of four preprints...

fields, ranging from algebra to probability, from functional analysis to number theory, etc. These connections shed the boundaries between combinatorics and...

used, such as algebra texts including 0, number theory and analysis texts excluding 0, logic and set theory texts including 0, dictionaries excluding...

Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that cannot...

have application to the solution of Diophantine equations, results in number theory have been scrutinised more than in other branches of mathematics to...